Symmetry breaking in the wake of a streamwise oscillating cylinder in density stratified fluid flows

The wake dynamics of a circular cylinder oscillating in the streamwise direction within a stably (density) stratified fluid is investigated using two-dimensional numerical simulations: Floquet stability analysis and dynamic mode decomposition. At a fixed Reynolds number ( $ \textit{Re}=175$ ) and forcing frequency ratio ( $f_d/f_{St}=1.6$ ), we examine the effects of the oscillation amplitude ( $0.1 \leqslant A_D \leqslant 0.6$ ) and the stratification strength ( $1 \leqslant \textit{Fr} \leqslant \infty$ ) on the wake structure and its symmetry breaking. In unstratified (homogeneous) flow ( $ \textit{Fr} = \infty$ ), the wake transitions from an asymmetric vortex street at low amplitudes to a symmetric state at higher amplitudes. This transition occurs via a Neimark–Sacker bifurcation, with Floquet analysis identifying a critical amplitude of $A_D = 0.455$ . In stratified flow, buoyancy forces improve symmetry and suppress vortex shedding for $A_D=0$ . At $ \textit{Fr} = 1$ , symmetry breaking first occurs at a threshold of $A_D = 0.246$ , associated with a period-doubling bifurcation and subharmonic antisymmetric vortex shedding, and persists only within a finite amplitude window ( $0.246 \lt A_D \lt 0.560$ ), beyond which the wake restabilises into a symmetric pattern. At a fixed small amplitude ( $A_D = 0.1$ ), a secondary critical transition is observed at $ \textit{Fr} = 1.52$ , marked by quasiperiodic antisymmetric shedding through a near-resonant Neimark–Sacker bifurcation. Stratification also influences force production: moderate stratification ( $ \textit{Fr} \approx 2$ ) minimises drag through enhanced pressure recovery and suppressed wake asymmetry. These results highlight the dual role of stratification in promoting or delaying symmetry-breaking instabilities and modifying wake dynamics. Critical transition thresholds are established, providing insight into buoyancy-modulated flow control strategies relevant to geophysical and engineering applications involving oscillating bodies in stratified environments.